Problem: Which of the following numbers is a multiple of 4? ${76,77,78,83,85}$
The multiples of $4$ are $4$ $8$ $12$ $16$ ..... In general, any number that leaves no remainder when divided by $4$ is considered a multiple of $4$ We can start by dividing each of our answer choices by $4$ $76 \div 4 = 19$ $77 \div 4 = 19\text{ R }1$ $78 \div 4 = 19\text{ R }2$ $83 \div 4 = 20\text{ R }3$ $85 \div 4 = 21\text{ R }1$ The only answer choice that leaves no remainder after the division is $76$ $ 19$ $4$ $76$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $4$ are contained within the prime factors of $76$ $76 = 2\times2\times19 4 = 2\times2$ Therefore the only multiple of $4$ out of our choices is $76$. We can say that $76$ is divisible by $4$.